717:
results for which we would know how to find a proof (or refutation), but we would be unable, or unwilling, to pay for finding such proofs, since “almost certainty” can be bought so much cheaper. I can envision an abstract of a paper, c. 2100, that reads : “We show, in a certain precise sense, that the
Goldbach conjecture is true with probability larger than 0.99999, and that its complete truth could be determined with a budget of $ 10B.”" Some people strongly disagree with Zeilberger's prediction; for example, it has been described as provocative and quite wrongheaded, whereas it has also been stated that choosing which theorems are interesting enough to pay for already happens as a result of funding bodies making decisions as to which areas of research to invest in.
1962:
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weight and has been written about by many notable mathematicians. Typically, they are motivated by a desire to set a research agenda to direct efforts to specific problems, or a wish to clarify, update and extrapolate the way that subdisciplines relate to the general discipline of mathematics and its possibilities. Examples of agendas pushing for progress in specific areas in the future, historical and recent, include
1998:
1986:
594:
and individual mathematical problems into the future is a widely debated topic; many past predictions about modern mathematics have been misplaced or completely false, so there is reason to believe that many predictions today will follow a similar path. However, the subject still carries an important
729:
writes about three stages: 1) at the moment computers are just slaves doing boring calculations, 2) soon databases of mathematical concepts and proof methods will lead to an intermediate stage where computers are very helpful with theorem proving but unthreatening, and 3) within a century computers
680:
writes in "The Proof is in the
Pudding. A Look at the Changing Nature of Mathematical Proof": "It is becoming increasingly evident that the delineations among “engineer” and “mathematician” and “physicist” are becoming ever more vague. It seems plausible that in 100 years we will no longer speak of
830:
predicted that by 2050 most numerical programs will be 99% intelligent wrapper and only 1% algorithm, and that the distinction between linear and non-linear problems, and between forward problems (one step) and inverse problems (iteration), and between algebraic and analytic problems, will fade as
716:
considers a time when computers become so powerful that the predominant questions in mathematics change from proving things to determining how much it would cost: "As wider classes of identities, and perhaps even other kinds of classes of theorems, become routinely provable, we might witness many
782:
writes: "Hilbert, I think, said that a subject is alive only if it has an abundance of problems. It is exactly this that makes combinatorics very much alive. I have no doubt that combinatorics will be around in a hundred years from now. It will be a completely different subject but it will still
663:
describes how the mathematics community and mathematical research activity is growing and states that this will mean changes in the way things are done: larger organisations mean more resources are spent on overheads (coordination and communication); in mathematics this would equate to more time
843:
in "Possible Trends in
Mathematics in the Coming Decades", says that traditional probability theory applies where global structure such as the Gauss Law emerges when there is a lack of structure between individual data points, but that one of today's problems is to develop methods for analyzing
748:
Different subjects of mathematics have very different predictions; for example, while every subject of mathematics is seen to be altered by the computer, some branches are seen to benefit from the use of technology to aid human achievement, while in others computers are predicted to completely
692:
is the use of computers to generate large data sets within which to automate the discovery of patterns which can then form the basis of conjectures and eventually new theories. The paper "Experimental
Mathematics: Recent Developments and Future Outlook" describes expected increases in computer
774:
throw some light on present trends and future directions. I have divided the causes into four groups: the influence of the computer; the growing sophistication of combinatorics; its strengthening links with the rest of mathematics; and wider changes in society. What is clear, though, is that
635:
writing in 1908 (English translation), "The true method of forecasting the future of mathematics lies in the study of its history and its present state". The historical approach can consist of the study of earlier predictions, and comparing them to the present state of the art to see how the
622:
The accuracy of predictions about mathematics has varied widely and has proceeded very closely to that of technology. As such, it is important to keep in mind that many of the predictions by researchers below may be misguided or turn out to be untrue.
681:
mathematicians as such but rather of mathematical scientists. It would not be at all surprising if the notion of “the
Department of Mathematics” at the college and university level gives way to “the Division of Mathematical Sciences”."
899:
is an enormous and diverse subject. Some indications of future research directions are given in "New Trends in
Mathematical Physics: Selected Contributions of the XVth International Congress on Mathematical Physics".
883:
is one of the fastest expanding areas of mathematics at the beginning of the 21st century. "Mathematics Is
Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better" is an essay by
647:, this leads to quite a bit of uncertainty in the future of mathematics. Also entailed by this is that successful predictions about future technology may also result in successful mathematical predictions.
654:
must also consider changes that are happening in the mathematical requirements of the workplace; course design will be influenced both by current and by possible future areas of application of mathematics.
636:
predictions have fared, e.g. monitoring the progress of
Hilbert's problems. A subject survey of mathematics itself however is now problematic: the sheer expansion of the subject gives rise to issues of
364:
824:
wrote "Predictions for scientific computing 50 years from now", which concluded with the theme that "Human beings will be removed from the loop" and writing in 2008 in
650:
Given the support of research by governments and other funding bodies, concerns about the future form part of the rationale of the distribution of funding.
959:
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everything becomes solved by iterative methods inside adaptive intelligent systems that mix and match and combine algorithms as required.
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The development of technology has also significantly impacted the outcomes of many predictions; because of the uncertain nature of the
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capabilities: better hardware in terms of speed and memory capacity; better software in terms of increasing sophistication of
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New Trends in
Mathematical Physics: Selected Contributions of the XVth International Congress on Mathematical Physics
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is outlined in "Future
Directions in Control, Dynamics, and Systems: Overview, Grand Challenges, and New Courses".
2029:
1880:
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1978:
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740:(both recipients of Fields Medal) don't agree with Gowers statements, especially those concerning "a threat".
1408:
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1248:"Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better"
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section 01Axx History of mathematics and mathematicians, subsection 01A67 is titled Future prospectives.
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1076:; Borwein, Jonathan M. (2001). "Experimental Mathematics: Recent Developments and Future Outlook".
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Future Directions in Control, Dynamics, and Systems: Overview, Grand Challenges, and New Courses
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was discussed in "The Prospects For Mathematical Logic In The Twenty-First Century", including
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in "Combinatorics entering the third millennium" organizes predictions for the future of
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where classical probability does not apply. Such methods might include advances in
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The Princeton Companion to Mathematics, Princeton University Press, 2008, Page 614
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1312:, Editors N. Alon, J. Bourgain, A. Connes, M Gromov, V. Milman, Springer, 2010,
1061:
The Proof is in the Pudding. A Look at the Changing Nature of Mathematical Proof
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1033:, Editors Richard A. Lesh, Eric Hamilton, James J. Kaput Routledge, 2007,
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1391:, forum for all topics related to the future of mathematical publishing.
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1169:"Creative Minds, Charmed Lives", Yu Kiang Leong, World Scientific, 2010
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combinatorics will continue to elude attempts at formal specification.
1105:"Theorems for a Price: Tomorrow’s Semi-Rigorous Mathematical Culture"
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1358:, Editors Mark Alber, Bei Hu, Joachim Rosenthal, Birkhäuser, 1997,
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Not only beyond Journals, not only beyond Papers. Beyond Theorems.
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The Prospects For Mathematical Logic In The Twenty-First Century
815:
626:
1371:, Editors Björn Engquist, Wilfried Schmid, Springer, 2001,
1345:, Edna Ernestine Kramer, Princeton University Press, 1982,
1250:, Joel E. Cohen, PLoS Biol, 2004 – biology.plosjournals.org
783:
flourish simply because it still has many, many problems".
1299:, V. I. Arnold, M. Atiyah, B. Mazur, AMS Bookstore, 2000,
1145:
Rough structure and classification, Timothy Gowers, 1999,
1238:, Richard M. Murray, European journal of control, 2003.
1050:
Trends in Mathematics: How they could Change Education?
661:
Trends in Mathematics: How they could Change Education?
1203:
Predictions for scientific computing 50 years from now
1000:
The honors class: Hilbert's problems and their solvers
1356:
Current and future directions in applied mathematics
1224:
Possible Trends in Mathematics in the Coming Decades
1123:
Proof and other dilemmas: mathematics and philosophy
984:
Atti del IV° Congresse internazionale dei Matematici
1031:
Foundations for the future in mathematics education
1147:https://www.dpmms.cam.ac.uk/~wtg10/gafavisions.ps
2016:
939:MAA Centenary Volume. Retrieved 7 February 2019.
968:Revue générale des sciences pures et appliquées
730:will be better than humans at theorem proving.
1205:, Lloyd N. Trefethen (Mathematics Today, 2000)
1416:
1072:
571:
365:
29:The examples and perspective in this article
970:19 (1908), pages 930–939. Also appeared in:
708:
1430:
1343:The nature and growth of modern mathematics
1226:, Mikhael Gromov, Notices of the AMS, 1998.
1158:Combinatorics entering the third millennium
816:Numerical analysis and scientific computing
684:
627:Motivations and methodology for speculation
1423:
1409:
1160:, Peter J. Cameron, Third draft, July 2001
937:"The Future of Mathematics: 1965 to 2065."
664:engaged in survey and expository writing.
578:
564:
372:
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1021:, Marja Makarow, ERCIM NEWS 30 April 2008
928:
926:
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743:
725:In "Rough structure and classification",
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1323:Reflections on the Future of Mathematics
988:International Congress of Mathematicians
910:List of unsolved problems in mathematics
720:
1297:Mathematics: frontiers and perspectives
891:
875:
2017:
1369:Mathematics unlimited: 2001 and beyond
1078:Mathematics unlimited: 2001 and beyond
1002:, Ben Yandell, A K Peters Ltd., 2002,
955:. Translation of the French original:
921:
827:The Princeton Companion to Mathematics
810:
590:The progression of both the nature of
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1985:
1329:, JUNE/JULY 2002, NOTICES OF THE AMS
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15:
1997:
1193:, Bulletin of Symbolic Logic, 2001.
976:Bulletin des Sciences mathématiques
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13:
1280:
617:Mathematics Subject Classification
14:
2041:
1382:
1113:16:4, pages 11–18, December 1994.
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638:mathematical knowledge management
1996:
1984:
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1339:, April 2008, Notices of the AMS
1019:Keynote – Mathematics Everywhere
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1881:Computational complexity theory
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868:A list of grand challenges for
1129:, Roger A. Simons, MAA, 2008,
1110:The Mathematical Intelligencer
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1:
986:. Lecture held at the Eighth
972:Circolo Matematico di Palermo
915:
43:and discuss the issue on the
1080:. Springer. pp. 51–66.
957:"L'avenir des mathématiques"
7:
1397:, Felix Breuer, 27 Feb 2012
953:"The Future of Mathematics"
903:
331:Science fiction prototyping
263:Reference class forecasting
10:
2046:
1931:Films about mathematicians
854:higher-dimensional methods
701:facilities; the mixing of
488:Relationship with sciences
1954:
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1500:Philosophy of mathematics
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1287:The Future Of Mathematics
709:Semi-rigorous mathematics
613:Millennium Prize Problems
1936:Recreational mathematics
1063:, Steven G. Krantz, 2008
799:, mathematical logic in
690:Experimental mathematics
685:Experimental mathematics
103:Global catastrophic risk
1821:Mathematical statistics
1811:Mathematical psychology
1781:Engineering mathematics
1715:Algebraic number theory
316:Exploratory engineering
206:Causal layered analysis
2030:History of mathematics
1967:Mathematics portal
1816:Mathematical sociology
1796:Mathematical economics
1791:Mathematical chemistry
1720:Analytic number theory
1601:Differential equations
1335:, Philip J. Davis and
1310:Visions in Mathematics
777:
744:Mathematics by subject
703:numerical and symbolic
668:Mathematics in general
652:Mathematical education
143:Historical materialism
1946:Mathematics education
1876:Theory of computation
1596:Hypercomplex analysis
772:
721:Automated mathematics
221:Cross impact analysis
1926:Informal mathematics
1806:Mathematical physics
1801:Mathematical finance
1786:Mathematical biology
1725:Diophantine geometry
1333:Henri’s Crystal Ball
1189:, Anand Pillay, and
1187:Alexander S. Kechris
990:, Rome, Italy, 1908.
933:Borwein, Jonathan M.
897:Mathematical physics
892:Mathematical physics
881:Mathematical biology
876:Mathematical biology
645:future of technology
453:Discrete mathematics
41:improve this article
31:may not represent a
1941:Mathematics and art
1851:Operations research
1606:Functional analysis
1264:Vladas Sidoravicius
811:Applied mathematics
387:Part of a series on
346:Technology scouting
93:Accelerating change
1886:Numerical analysis
1495:Mathematical logic
1490:Information theory
1266:, Springer, 2009,
962:2013-12-27 at the
858:inverse scattering
822:Lloyd N. Trefethen
793:mathematical logic
791:In the year 2000,
787:Mathematical logic
605:Hilbert's problems
554:Mathematics Portal
336:Speculative design
216:Consensus forecast
211:Chain-linked model
173:Resource depletion
2012:
2011:
1611:Harmonic analysis
1377:978-3-540-66913-5
1364:978-0-8176-3956-3
1351:978-0-691-02372-4
1318:978-3-0346-0421-5
1305:978-0-8218-2697-3
1272:978-90-481-2809-9
1135:978-0-88385-567-6
1039:978-0-8058-6056-6
1008:978-1-56881-216-8
673:Subject divisions
609:Langlands program
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268:Scenario planning
131:Space exploration
62:
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1871:Computer science
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801:computer science
753:Pure mathematics
749:replace humans.
714:Doron Zeilberger
697:; more advanced
678:Steven G. Krantz
601:Erlangen program
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311:Design fiction
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283:Trend analysis
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35:of the subject
28:
26:
19:
9:
6:
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3:
2:
2042:
2031:
2028:
2026:
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2005:
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1863:Computational
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1634:Combinatorics
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1586:Real analysis
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1334:
1331:
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1327:Felix Browder
1324:
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989:
985:
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945:
938:
934:
929:
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889:
887:
886:Joel E. Cohen
882:
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842:
835:Data analysis
832:
829:
828:
823:
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806:
802:
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794:
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780:Béla Bollobás
776:
771:
769:
768:combinatorics
765:
764:Peter Cameron
758:Combinatorics
750:
741:
739:
735:
731:
728:
718:
715:
706:
704:
700:
699:visualization
696:
691:
682:
679:
665:
662:
658:
657:László Lovász
653:
648:
646:
641:
639:
634:
631:According to
624:
620:
618:
614:
610:
606:
602:
598:
593:
581:
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449:
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429:Number theory
427:
426:
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278:Threatcasting
276:
274:
271:
269:
266:
264:
261:
259:
256:
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251:
249:
248:Futures wheel
246:
244:
241:
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214:
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209:
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202:
199:
198:
197:
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184:
183:Swanson's law
181:
179:
176:
174:
171:
169:
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159:
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154:
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149:
146:
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137:
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129:
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109:
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81:
77:
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72:
69:
66:
65:
56:
46:
42:
36:
34:
27:
18:
17:
2001:
1989:
1977:
1958:
1891:Optimization
1753:Differential
1677:Differential
1644:Order theory
1639:Graph theory
1543:Group theory
1454:
1255:
1243:
1231:
1219:
1210:
1198:
1174:
1165:
1153:
1141:
1118:
1108:
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1077:
1068:
1056:
1045:
1026:
1014:
995:
983:
979:
975:
971:
967:
944:
895:
879:
867:
838:
825:
819:
805:proof theory
790:
778:
773:
761:
747:
732:
724:
712:
688:
676:
660:
649:
642:
630:
621:
589:
243:Future-proof
115:
50:
30:
2003:WikiProject
1846:Game theory
1826:Probability
1563:Homological
1553:Multilinear
1533:Commutative
1510:Type theory
1477:Foundations
1433:mathematics
1127:Bonnie Gold
734:Terence Tao
597:Felix Klein
592:mathematics
519:Linguistics
509:Computation
504:Geosciences
467:Probability
393:Mathematics
297:forecasting
291:Technology
201:Backcasting
178:Singularity
158:Moore's law
116:Mathematics
2019:Categories
1831:Statistics
1710:Arithmetic
1672:Arithmetic
1538:Elementary
1505:Set theory
1291:André Weil
916:References
797:set theory
695:algorithms
611:, and the
529:Philosophy
472:Statistics
462:Set theory
326:Hype cycle
293:assessment
192:Techniques
53:April 2021
1758:Geometric
1748:Algebraic
1687:Euclidean
1662:Algebraic
1558:Universal
1389:Math 2.0
1262:, Editor
1082:CiteSeerX
839:In 1998,
820:In 2000,
762:In 2001,
705:methods.
615:. In the
534:Education
524:Economics
499:Chemistry
238:Foresight
45:talk page
33:full view
1979:Category
1735:Topology
1682:Discrete
1667:Analytic
1654:Geometry
1626:Discrete
1581:Calculus
1573:Analysis
1528:Abstract
1467:Glossary
1450:Timeline
1103:(1994).
980:Scientia
960:Archived
951:(1908).
935:(2013).
904:See also
448:Analysis
444:Calculus
434:Geometry
163:Peak oil
136:Universe
84:Concepts
1991:Commons
1773:Applied
1743:General
1520:Algebra
1445:History
514:Biology
494:Physics
439:Algebra
402:History
126:Climate
107:Future
39:Please
1692:Finite
1548:Linear
1455:Future
1431:Major
1375:
1362:
1349:
1316:
1303:
1293:, 1950
1270:
1133:
1084:
1037:
1006:
982:; and
803:, and
226:Delphi
1919:lists
1462:Lists
1435:areas
966:. in
659:, in
458:Logic
422:Areas
407:Index
111:Earth
1373:ISBN
1360:ISBN
1347:ISBN
1314:ISBN
1301:ISBN
1268:ISBN
1131:ISBN
1035:ISBN
1004:ISBN
856:and
736:and
474:and
460:and
446:and
295:and
121:Race
599:'s
341:TRL
321:FTA
2021::
1325:,
1289:,
1185:,
1181:,
1125:,
1107:.
978:;
974:;
923:^
888:.
860:.
852:,
807:.
770::
640:.
607:,
603:,
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1274:.
1090:.
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366:t
359:v
55:)
51:(
47:.
37:.
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